Probability is a branch of mathematics that deals with the chance or likelihood of an event occurring. In this worksheet, we’ll explore some basic concepts of probability and practice solving problems.
Probability Basics
Probability is a number between 0 and 1 that represents the chance of an event happening. A probability of 0 means the event is impossible, while a probability of 1 means the event is certain.
There are three types of events:
- Independent events: The outcome of one event does not affect the outcome of another event.
- Dependent events: The outcome of one event affects the outcome of another event.
- Mutually exclusive events: The events cannot occur at the same time.
Probability Formulas
- Theoretical probability: The number of favorable outcomes divided by the total number of possible outcomes.
P(event) = Number of favorable outcomes / Total number of possible outcomes
- Experimental probability: The number of times an event occurs divided by the total number of trials.
P(event) = Number of times event occurs / Total number of trials
Practice Problems
- A fair coin is flipped. What is the probability of getting heads?
Solution: There are 2 possible outcomes: heads or tails. The number of favorable outcomes is 1 (getting heads). The total number of possible outcomes is 2.
P(heads) = 1 / 2 = 0.5
- A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. What is the probability of drawing a blue marble?
Solution: There are 10 possible outcomes (5 red, 3 blue, and 2 green). The number of favorable outcomes is 3 (drawing a blue marble).
P(blue) = 3 / 10 = 0.3
- A spinner has 8 equal sections, numbered 1 to 8. What is the probability of spinning a number greater than 5?
Solution: There are 8 possible outcomes. The number of favorable outcomes is 3 (spinning a 6, 7, or 8).
P(greater than 5) = 3 / 8 = 0.375
- A student has a 75% chance of passing a test. If they take the test 4 times, what is the probability of passing all 4 times?
Solution: Since the events are independent, we can multiply the probabilities.
P(passing all 4 times) = 0.75 × 0.75 × 0.75 × 0.75 = 0.3164
Notes
📝 Note: When calculating probability, make sure to simplify the fraction or round the decimal to the nearest hundredth.
📝 Note: When events are independent, we can multiply the probabilities to find the probability of multiple events occurring.
FAQ
What is the difference between theoretical and experimental probability?
+Theoretical probability is based on the number of favorable outcomes divided by the total number of possible outcomes, while experimental probability is based on the number of times an event occurs divided by the total number of trials.
What is the probability of an impossible event?
+The probability of an impossible event is 0.
What is the probability of a certain event?
+The probability of a certain event is 1.
Recap
In this worksheet, we explored the basics of probability and practiced solving problems. We learned about theoretical and experimental probability, independent and dependent events, and mutually exclusive events. We also practiced calculating probabilities using formulas and solving problems with different types of events.
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